Aptitude questions and answers on time and works

1) Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

1. days.
2. days.
3. days.
4. days.

Explanation:

Worker A completes the task in 8 days. So, in one day, he will complete part of the task.

So, A's one day work = Similarly, B's one day work = ∴ (A+B)'s one day work =  of the task is completed in one day so both will complete the whole task in days

2) Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?

1. 13 days
2. 14 days
3. 15 days
4. 16 days

Explanation:

Vikas and Mohan together can complete the task in 6 days. So, in one day, they will complete part of the task.

Therefore, (Vikas + Mohan)'s one day work will be = Similarly, Vikas's one day work = Therefore, Mohan's one day work =  In one day Mohan completes the part of the work so he will complete the entire work in 15 days.

3) A can do work in 10 days and B can do the same work in 15 days. If they start working together but stop working after four days, find the fraction of the work that is left.

1. 2. 3. 4. Explanation:

A's one day work = B's one day work = (A + B)'s one day work =  A and B's four-day work = Therefore, the remaining work = 4) Peter is twice as good as a workman as Tom. When they work together they can finish a task in 16 days. If Tom works alone, in many days he will complete the task?

1. 46 days
2. 48 days
3. 50 days
4. 52 days

Explanation:

(Peter + Tom)'s one-day work = 1/16

As per the question, Peter can finish twice as much work as finished by Tom in a given duration of time.

Therefore, of their one day's work will be completed by Peter and of their one day's work will be completed by Tom.

So, Tom's one day work will be = So, Tom will take 48 days to complete the task.

5) A can do a job in 12 days and B can do the same job in 10 days. With the help of C, they can do the same job in 4 days. In how many days C alone can do this job?

1. 15 days
2. 14 days
3. 13 days
4. 12 days

Explanation:

A's one day work = B's one day work = (A+B+C)'s one day work = Therefore, C's one day work = (A+B+C)'s one day work (A+B)'s one day work

So, C's one day work =   So, C will complete the work in 15 days.

6) A, B, C can do a job in 10, 20, and 40 days respectively. In how many days A can complete the job if he is assisted by B and C every third day?

1. 8 days
2. 7 days
3. 9 days
4. 6 days

Explanation:

A's one day work = B's one day work = C's one day work = (A+B+C)'s one day work = Work done in three days will be the sum of A's two-day work and (A+B+C)'s one-day work.

A's two-day work = Therefore, the work is done in three days = 3/8 part of the job is done in 3 days.

The entire job will be done by A in = 3 x 7) If 5 men can color 50-meter long cloth in 5 days, in many days 4 men can color a 40-meter long cloth?

1. 5 days
2. 6 days
3. 4 days
4. 3 days

Explanation:

5 men color 50-meter long cloth in 5 days.

1 man will colour = 10-meter long cloth in five days.

So, in one day one man can colour = 2-meter long cloth.

Now, as per question 4 men are supposed to color the 40-meter long cloth.

One man has to color the = 10-meter cloth

For 2-meter long cloth, one man takes 1 day

So, to paint a 10-meter long cloth he will take = As 4 men are working together so 40 m long cloth will be colored in 5 days

8) If 4 men can finish 4 times of work in 4 days, in how many days 6 men can finish the 6 times of same work?

1. 3 days
2. 4 days
3. 5 days
4. 6 days

Explanation:

4 men can finish 4 times of work in four days.

Therefore, one man can finish the one time of work in four days.

So, 6 men will finish the six times of work in the same time (4 days)

9) A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

1. 6.2 days
2. 6.6 days
3. 7 days
4. 7.2 days

Explanation:

B is 50% more efficient than A so he will take less time to do a piece of work.

Therefore, the ratio of the time taken by A and B = Let B takes X days to do the job. 3X =20

X = 6.6 days

10) A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?

1. 15 days
2. 16 days
3. 17 days
4. 18 days

Explanation:

A's one day work = A's ten-day work = So the remaining work would be = B's one day work = A and B's one day work =  of the job will be done by them in one day.

So, the remaining job = 8 days

Therefore, the total number of days required to do the job would be = 10 + 8 = 18 days

11) A can do a piece of work in 6 days working 8 hours a day. B can do the same work in 4 days working 6 hours a day. If they work together 8 hours a day, in how many days they will do this work?

1. 3 days
2. 3.5 days
3. 2 days
4. 2.5 days

Explanation:

A can complete the work in, 6 x 8 = 48 hour

B can complete the same work in = 4 x 6 = 24 hours

A's one hour work = B's one hour work = (A +B)'s one hour work = They will complete So, the entire work will be completed in 1 ∗ 144 = 144 hours
9        9

Both work 8 hours a day so the number of days required to complete the work = = 2 days

12) A can finish a work in 6 days and B can finish the same work in 8 days. A and B charge Rs. 2800 for the work. If with the help of C they complete the work in 3 days, how much they will pay to C?

1. Rs. 350
2. Rs. 345
3. Rs. 340
4. Rs. 320

Explanation:

A's one hour work = 1
6

B's one hour work = 1
8

(A +B)'s one hour work = 1 + 1 = 7
6    8   24

(A+B+C)'s one-day work = 1
3

Therefore, C's one day work = 1 - 7 =    1
3    24   24

The ratio of A, B, and C's wages will be equal to the ratio of work done by them in one day.

A's wages: B's wages: C's wages = 1 : 1 : 1
6    8  24

C's share of three days = 3 * C's share for one day

= 3 ∗ (1 ∗ 2800) = 350
24

13) 5 men undertook a piece of work and finished half the work in 18 days if two men drop out, in how many days the remaining work will be completed?

1. 30 days
2. 32 days
3. 34 days
4. 36 days

Explanation:

5 men completed half of the work in 18 days so the entire work will be completed in 36 days.

5 men' one day work will be = One man's one day work = Two men drop out, so the three men have to complete the remaining work.

Three men's one day work will be =  part of the work is completed by three men in one day

Therefore, the remaining part of the work will be completed in = 30 Days.

14) If 5 workers can paint a house in 9 days, in how many days 3 workers can complete the same task?

1. 13 days
2. 14 days
3. 15 days
4. 16 days

Explanation:

Using formula: M1D1W2 =M2D2W1

We have = 5∗9∗W2 = 3∗D2∗W1

W2 = W1 as the task is the same in both cases, so the amount of work to be done would be the same.

Therefore, we have 5 ∗ 9 = 3 ∗ D2

45 = 3∗ D2

D2 =   45   =   15days
3

15) A group of workers undertakes a task. They can complete the task in 30 days. If 5 of them did not turn for the work and the remaining workers complete the task in 40 days, find the original number of workers.

1. 25 days
2. 23 days
3. 21 days
4. 20 days

Explanation:

Let the original number of workers = X

X workers can complete the work in 30 days. And (X - 50) complete the same task in 40 days.

Apply formula: M1D1W2 =M2D2W1

W1=W2 as the task is the same in both the cases.

Therefore, X * 30 = (X - 5) * 40

30 X = 40X - 200

200 = 40X -30X

200 = 10 X

=   200   =   20days
10

16) 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

1. 1
2. 3
3. 5

Explanation:

 1 woman's 1 day's work 1 child's 1 day's work = 1/70 = 1/140. (5 women +10 children)'s 1 day's work = (5/70+10/140) = (1/14+1/14) = 1/7. 5 women + 10 children will complete the work in 7 days.

17) A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work in 44 days. In how many days shall B finish the whole work alone?

1. 30 days
2. 40 days
3. 60 days
4. 70 days

Explanation:

 A's 1 day's work = x B's 1 day's work = y Then, x+y = 1/30 and 16x+44y = 1. Solving these two equations, we get x=1/10 and y=1/60

Therefore, B alone finish work in 60 days.

18) Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but indepently, to do the same job?

1. 2*4/9
2. 4*4/9
3. 5*4/9
4. 4*2/9

Explanation:

 A's 1 day's work = 1/8 B's 1 day's work = 1/10 (A+B)'s 1 day's work = (1/8 + 1/10) = 9/40. Both A and B will finish the work in = 40 / 9 ‹=›4×4/9

19) A, B and C are employed to do a piece of work for Rs.529. A and B together are supposed to do 19/23 of the work and Band C together 8/23 of the work. What amount should A be paid?

1. ₹ 315
2. ₹ 345
3. ₹ 355
4. ₹ 375

Explanation:

 Work done by A So, A's share=Rs.(15/23 x 529) =(1 - 8/23) = 15/23 A : (B+C) =(15/23 : 8/23) = 15 : 8 = Rs.345.

20) A can do a piece of work in 10 days, and B can do the same work in 20 days. With the help of C, they finished the work in 4 days. C can do the work in how many days, working alone?

1. 5 days

2. 10 days

3. 15 days

4. 20 days

Explanation:

Their combined 4 day work = 4(1/10 + 1/15) = 12/20 = 3/5.

Remaining work = 1 – 3/5 = ⅖.

This means C did 2/5 work in 4 days, hence he can finish the complete work in 5/2 × 4 = 10 days.

21) A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?

1. 2 days

2. 3 days

3. 4 days

4.  5 days

Explanation:

A's work in 9 days = 9/12 = 3/4. Remaining work = 1/4.
This work was done by B in 1/4 × 16 = 4 days.
∴ B would have joined A after 9 – 4 = 5 days.

22) A, B, C, and D can do a piece of work in 20 days. If A and B can do it together in 50 days, and C alone in 60 days, find the time in which D alone can do it.

1. 150 days
2. 120 days
3. 90 days
4. 75 days

Explanation:

D alone will take 1/20 – 1/50 – 1/60 = 4/300 = 1/75
⇒ 75 days to complete the work.

23) A, B, and C can do a piece of work in 8 days. B and C together do it in 24 days. B alone can do it in 40 days. In what time will it be done by C working alone?

1. 25
2. 24
3. 60
4. 30

Explanation:

B & C do this work in 24 days.

B alone does this work in 40 days.

C alone will take 1/24 – 1/40 = 2/120=1/60 ⇒ 60 days to finish the work.

24) Tejas and Nikhil can do a piece of work in 70 and 60 days respectively. They began the work together, but Tejas leaves after some days and Nikhil finished the remaining work in 47 days. After how many days did Tejas leave?

1. 16 days
2. 7 days
3. 18 days
4. 19 days

Explanation:

Nikhil would have done 47/60 work in 47 days

The remaining work i.e. 13/60 must have been done by Tejas and Nikhil together

They can do the whole work in 60 × 70 / (60 + 70) = 60 × 70/130 = 420/13 days.

So, they would have done 13/60 work in 420/13 × 13/60 = 7 days

Therefore, Tejas left the work after 7 days.

25) Ajay and Vijay undertake to do a piece of work for Rs. 480. Ajay alone can do it in 75 days while Vijay alone can do it in 40 days. With the help of Pradeep, they finish the work in 25 days. How much should Pradeep get for his work?

1. 20
2. 360
3. 100
4. 60

Explanation:

In 24 days, they would have done 1/3 and 5/8 of the work.

The remaining work is 1 – (1/3 + 5/8) = 1/24.

This means Pradeep has done 1/24th of the work, so he should be paid 1/24th of the amount

i.e. 480 × 1/24 = Rs. 20 is the answer.

26) Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes. For how many minutes was first pipe open?

1. 8 min
2. 6 min
3. 7 min
4. 10 min

Explanation:

Second pipe is opened for 10 minutes.

So , part of tank filled by the second pipe = 10/20=1/2.

So, 1 -1 = 1  tank is filled by first pipe. First pipe can fill 1  of tank in 1 * 12 = 6minutes.
2    2                                                                     2                  2

So, the first pipe is opened for 6 minutes.

27) Two pipes can fill a tank in 15 minutes and 12 minutes. The outlet pipe can empty the tank in 20 minutes. If all the pipes are opened when, the tank is empty, then in how many minutes will it take to fill the tank?

1. 12
2. 13
3. 10
4. 11

Explanation:

Part of tank filled by all three pipes in one minute =

1/15+ 1/12 – 1/20  =  8+10-6/120 = 18-6/120

= 1/10

So, the tank becomes full in 10 minutes.

28) Pipe A can fill a tank in 12 hours. Due to a leak at the bottom it takes 20 hours to fill the tank. In what time the leak alone can empty the full tank?

1. 18 hours
2. 23 hours
3. 28 hours
4. 30 hours

Explanation:

Let leak can empty the full tank in x hours.

1/12-  1/x =  1/12   => 1/12 – 1/20 = 1

5-3= 1

60 - 30= 30

x= 30 hours

29) If A is thrice as fast as B and together can do a work in 21 days. In how many days A alone can do the work?

1. 36
2. 28
3. 42
4. 52

Explanation:

Exp: A’s one day’s work= 1/x

B’s one day’s work= 1/3x

A + B’s one day’s work= 1/x  + 1/3x  = 1/21

= 3+1/3x = 4/3x  = 1/21

x =  21*4/3 = 28

30) 9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?

1. 18
2. 9
3. 10
4. 8